I’d like to cut a rectangle into a 3×4 grid of squares. To minimise the number of cuts, should I cut three long strips first, or four short str

Any way you cut it

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2024-11-16 12:30:04

I’d like to cut a rectangle into a 3×4 grid of squares. To minimise the number of cuts, should I cut three long strips first, or four short strips? Does it matter?

Here’s the talk I gave at this year’s Big MathsJam Gathering. I called it Please don’t overthink this (I already have)

Recently I presented a maths workshop for some year 3/4 kids in a local school. For those outside England and Wales, that means kids aged 7 to 9.

In order to do this, I needed lots of paper squares. The school aren’t providing any material themselves (or paying for my time…) so I want to do this on the cheap. So I’ve ruled out just buying lots of origami paper.

The most obvious way that occurred to me was to cut a strip off the long side to end up with a 210mm square, and then halve that in each direction until I get squares of a suitable size. I thought that halving once would give me 105mm squares, which feel about the right size.

Then I realised that 210 is 3×70, and 297 is only a little bit more than 280 = 4×70, so I could get 12 70mm squares out of each sheet, only leaving a little strip.

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